{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "786e86bd",
   "metadata": {},
   "source": [
    "# 06 - Effect Heterogeneity\n",
    "\n",
    "\n",
    "## From ATE to CATE\n",
    " \n",
    " \n",
    "## Why Prediction is not the Answer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f6fc230",
   "metadata": {},
   "source": [
    "## CATE with Regression\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "225ef0c5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:40.886176Z",
     "start_time": "2023-06-26T13:25:38.992451Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib\n",
    "\n",
    "from cycler import cycler\n",
    "\n",
    "color=['0.0', '0.4', '0.8']\n",
    "default_cycler = (cycler(color=color))\n",
    "linestyle=['-', '--', ':', '-.']\n",
    "marker=['o', 'v', 'd', 'p']\n",
    "\n",
    "plt.rc('axes', prop_cycle=default_cycler)\n",
    "\n",
    "matplotlib.rcParams.update({'font.size': 18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "66e32dce",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:40.906851Z",
     "start_time": "2023-06-26T13:25:40.887890Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rest_id</th>\n",
       "      <th>day</th>\n",
       "      <th>month</th>\n",
       "      <th>weekday</th>\n",
       "      <th>weekend</th>\n",
       "      <th>is_holiday</th>\n",
       "      <th>is_dec</th>\n",
       "      <th>is_nov</th>\n",
       "      <th>competitors_price</th>\n",
       "      <th>discounts</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>2016-01-01</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>2.88</td>\n",
       "      <td>0</td>\n",
       "      <td>79.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>2016-01-02</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>2.64</td>\n",
       "      <td>0</td>\n",
       "      <td>57.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2016-01-03</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>2.08</td>\n",
       "      <td>5</td>\n",
       "      <td>294.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>2016-01-04</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>3.37</td>\n",
       "      <td>15</td>\n",
       "      <td>676.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>2016-01-05</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>3.79</td>\n",
       "      <td>0</td>\n",
       "      <td>66.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   rest_id         day  month  weekday  weekend  is_holiday  is_dec  is_nov  \\\n",
       "0        0  2016-01-01      1        4    False        True   False   False   \n",
       "1        0  2016-01-02      1        5     True       False   False   False   \n",
       "2        0  2016-01-03      1        6     True       False   False   False   \n",
       "3        0  2016-01-04      1        0    False       False   False   False   \n",
       "4        0  2016-01-05      1        1    False       False   False   False   \n",
       "\n",
       "   competitors_price  discounts  sales  \n",
       "0               2.88          0   79.0  \n",
       "1               2.64          0   57.0  \n",
       "2               2.08          5  294.0  \n",
       "3               3.37         15  676.5  \n",
       "4               3.79          0   66.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/daily_restaurant_sales.csv\")\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "eef44db5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:41.075032Z",
     "start_time": "2023-06-26T13:25:40.908219Z"
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "\n",
    "X = [\"C(month)\", \"C(weekday)\", \"is_holiday\", \"competitors_price\"]\n",
    "regr_cate = smf.ols(f\"sales ~ discounts*({'+'.join(X)})\",\n",
    "                    data=data).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bd1a3920",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:41.137457Z",
     "start_time": "2023-06-26T13:25:41.076650Z"
    }
   },
   "outputs": [],
   "source": [
    "ols_cate_pred = (\n",
    "    regr_cate.predict(data.assign(discounts=data[\"discounts\"]+1)) \n",
    "    -regr_cate.predict(data)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "619f9511",
   "metadata": {},
   "source": [
    "## Evaluating CATE Predictions\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a91f7cb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:41.146365Z",
     "start_time": "2023-06-26T13:25:41.140384Z"
    }
   },
   "outputs": [],
   "source": [
    "train = data.query(\"day<'2018-01-01'\")\n",
    "test = data.query(\"day>='2018-01-01'\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e5f296fe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:41.236836Z",
     "start_time": "2023-06-26T13:25:41.147474Z"
    }
   },
   "outputs": [],
   "source": [
    "X = [\"C(month)\", \"C(weekday)\", \"is_holiday\", \"competitors_price\"]\n",
    "regr_model = smf.ols(f\"sales ~ discounts*({'+'.join(X)})\",\n",
    "                     data=train).fit()\n",
    "\n",
    "cate_pred = (\n",
    "    regr_model.predict(test.assign(discounts=test[\"discounts\"]+1)) \n",
    "    -regr_model.predict(test)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4a64072b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.102979Z",
     "start_time": "2023-06-26T13:25:41.238561Z"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "X = [\"month\", \"weekday\", \"is_holiday\", \"competitors_price\", \"discounts\"]\n",
    "y = \"sales\"\n",
    "\n",
    "np.random.seed(1)\n",
    "ml_model = GradientBoostingRegressor(n_estimators=50).fit(train[X],\n",
    "                                                          train[y])\n",
    "\n",
    "ml_pred = ml_model.predict(test[X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2fa967ec",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.107845Z",
     "start_time": "2023-06-26T13:25:42.104174Z"
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "test_pred = test.assign(\n",
    "    ml_pred=ml_pred,\n",
    "    cate_pred=cate_pred,\n",
    "    rand_m_pred=np.random.uniform(-1, 1, len(test)),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9d57f5d0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.115514Z",
     "start_time": "2023-06-26T13:25:42.108978Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rest_id</th>\n",
       "      <th>day</th>\n",
       "      <th>sales</th>\n",
       "      <th>ml_pred</th>\n",
       "      <th>cate_pred</th>\n",
       "      <th>rand_m_pred</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>731</th>\n",
       "      <td>0</td>\n",
       "      <td>2018-01-01</td>\n",
       "      <td>251.5</td>\n",
       "      <td>236.312960</td>\n",
       "      <td>41.355802</td>\n",
       "      <td>0.392938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>732</th>\n",
       "      <td>0</td>\n",
       "      <td>2018-01-02</td>\n",
       "      <td>541.0</td>\n",
       "      <td>470.218050</td>\n",
       "      <td>44.743887</td>\n",
       "      <td>-0.427721</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>733</th>\n",
       "      <td>0</td>\n",
       "      <td>2018-01-03</td>\n",
       "      <td>431.0</td>\n",
       "      <td>429.180652</td>\n",
       "      <td>39.783798</td>\n",
       "      <td>-0.546297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>734</th>\n",
       "      <td>0</td>\n",
       "      <td>2018-01-04</td>\n",
       "      <td>760.0</td>\n",
       "      <td>769.159322</td>\n",
       "      <td>40.770278</td>\n",
       "      <td>0.102630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>735</th>\n",
       "      <td>0</td>\n",
       "      <td>2018-01-05</td>\n",
       "      <td>78.0</td>\n",
       "      <td>83.426070</td>\n",
       "      <td>40.666949</td>\n",
       "      <td>0.438938</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     rest_id         day  sales     ml_pred  cate_pred  rand_m_pred\n",
       "731        0  2018-01-01  251.5  236.312960  41.355802     0.392938\n",
       "732        0  2018-01-02  541.0  470.218050  44.743887    -0.427721\n",
       "733        0  2018-01-03  431.0  429.180652  39.783798    -0.546297\n",
       "734        0  2018-01-04  760.0  769.159322  40.770278     0.102630\n",
       "735        0  2018-01-05   78.0   83.426070  40.666949     0.438938"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pred[[\"rest_id\", \"day\", \"sales\",\n",
    "           \"ml_pred\", \"cate_pred\", \"rand_m_pred\"]].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "353ebb42",
   "metadata": {},
   "source": [
    "## Effect by Model Quantile\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "97b983d8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.137748Z",
     "start_time": "2023-06-26T13:25:42.116681Z"
    }
   },
   "outputs": [],
   "source": [
    "from toolz import curry\n",
    "\n",
    "@curry\n",
    "def effect(data, y, t):\n",
    "        return (np.sum((data[t] - data[t].mean())*data[y]) /\n",
    "                np.sum((data[t] - data[t].mean())**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c5a4a71f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.142618Z",
     "start_time": "2023-06-26T13:25:42.138931Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.16196368039615"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "effect(test, \"sales\", \"discounts\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "71f0118f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.161264Z",
     "start_time": "2023-06-26T13:25:42.144053Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cate_pred_quantile\n",
       "17.50    20.494153\n",
       "23.93    24.782101\n",
       "26.85    27.494156\n",
       "28.95    28.833993\n",
       "30.81    29.604257\n",
       "32.68    32.216500\n",
       "34.65    35.889459\n",
       "36.75    36.846889\n",
       "39.40    39.125449\n",
       "47.36    44.272549\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def effect_by_quantile(df, pred, y, t, q=10):\n",
    "    \n",
    "    # makes quantile partitions\n",
    "    groups = np.round(pd.IntervalIndex(pd.qcut(df[pred], q=q)).mid, 2) \n",
    "    \n",
    "    return (df\n",
    "            .assign(**{f\"{pred}_quantile\": groups})\n",
    "            .groupby(f\"{pred}_quantile\")\n",
    "            # estimate the effect on each quantile\n",
    "            .apply(effect(y=y, t=t))) \n",
    "\n",
    "\n",
    "effect_by_quantile(test_pred, \"cate_pred\", y=\"sales\", t=\"discounts\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0dae115c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.431474Z",
     "start_time": "2023-06-26T13:25:42.162557Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, sharey=True, figsize=(15, 4))\n",
    "for m, ax in zip([\"rand_m_pred\", \"ml_pred\", \"cate_pred\"], axs):\n",
    "    effect_by_quantile(test_pred, m, \"sales\", \"discounts\").plot.bar(ax=ax)\n",
    "    ax.set_ylabel(\"Effect\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0966723b",
   "metadata": {},
   "source": [
    "## Cumulative Effect\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "39ea9ae3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.437357Z",
     "start_time": "2023-06-26T13:25:42.435301Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "np.set_printoptions(linewidth=80, threshold=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "94f06f36",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.545843Z",
     "start_time": "2023-06-26T13:25:42.438541Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([49.65116279, 49.37712454, 46.20360341, ..., 32.46981935, 32.33428884,\n",
       "       32.16196368])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cumulative_effect_curve(dataset, prediction, y, t,\n",
    "                            ascending=False, steps=100):\n",
    "    size = len(dataset)\n",
    "    ordered_df = (dataset\n",
    "                  .sort_values(prediction, ascending=ascending)\n",
    "                  .reset_index(drop=True))\n",
    "    \n",
    "    steps = np.linspace(size/steps, size, steps).round(0)\n",
    "    \n",
    "    return np.array([effect(ordered_df.query(f\"index<={row}\"), t=t, y=y)\n",
    "                     for row in steps])\n",
    "\n",
    "cumulative_effect_curve(test_pred, \"cate_pred\", \"sales\", \"discounts\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5952ea80",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:42.940453Z",
     "start_time": "2023-06-26T13:25:42.546937Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcb7b4a8c50>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lvETEWx3f4nK5qKmpoaioiIKCAkpKSoiPj6d79+46YbdSSinVQpp4qWaFhYURGxtLVlYW3bp1o6CggLy8PDZv3kxsbKy3bpjdbtfirEoppdRB6CelClh4eDjdunUjIyOD/fv3e1vB8vPzAbyJmFW6IiYmRlvElFJKKR+aeKkWCwsLIz09nfT0dFwuF5WVlZSXl1NRUUFBQYH3qkirtcxKwqKjo72LJmRKKaW6Ik281CEJCwvzdjeCe9Lu6upqqqqqvMv+/ftxuVx+j4uOjiYuLs47z6S2jimllOoKNPFSbUpEiI2NJTY2ltTUVMCdjNXV1VFdXU1NTQ01NTU4HA7KysooKioC3N2Ydrud+Ph4EhMTtVVMKaXUYUkTLxV0IkJkZCSRkZHeljFwJ2Q1NTVUVFR4l9LSUvbs2UNUVBSJiYkkJiYSExNDREQEYWFhmowppZTq1DTxUiEjIt5CrWlpaQDU1NRQWlpKWVkZ+/fvp6CgwG//8PBwIiIivImc722rpU2TM6WUUh2VJl6qQ4mOjiYjI4OMjAxcLhcVFRXU1tZSV1dHfX09dXV11NXV4XQ6qaiowOl0+k1xFBERQUJCAomJiSQkJGiJC6WUUh2KfiqpDissLIyEhIRm9zHG4HK5cDqdVFZWUlpaSmlpqXfsmO8Vlb4/w8PD2+MpKKWUUn408VKdmtX9GB4eTkxMDKmpqRhjvElYZWUlFRUV3kTMYrPZ/Iq/aiKmlFKqPQQ98RKRcGA1kGOMmSQiKcDLQDawA5hqjCk+8BGUahkR8ZapsFhTH1lzUJaXl5Ofn09eXh4AcXFxjWqNRUdHa1elUkqpNtUenyo3ABsBq8/oVuBjY8y9InKr5/4t7RCH6sKsYq6xsbHeuSjr6+v9ir+WlZXhdDr9HhcZGYnNZvMWgo2NjdVSF0oppVotqImXiPQEJgJ/B/7oWT0FGO+5vRBYhiZeKgTCw8NJSEjwG0fm2zJWXV2Nw+GgqqqK0tJSv8daV1JGRUV5y2QkJiYSFhbW3k9DKaVUJxLsFq/5wM1AvM+6TGNMLoAxJldEMpp6oIhcDVwN0Lt37yCHqZSbb8uYL5fLhcPhwOFwUFtbS21tLU6nk+rqasrKyigoKCA8PJzk5GRSUlKw2+3aKqaUUqqRoCVeIjIJyDfGrBGR8S19vDHmCeAJgNGjR5uD7K5UUIWFhREXF0dcXFyjbcYYysvLvROHFxYWEhUVRUJCQqMrKkWE+vp6nE4nTqeTuro6XC4X0dHR3tYzTdiUUurwddDES0Q+NsZMONi6JpwATBaRs4AYIEFEngfyRKS7p7WrO5Df2uCV6ghExNtlWV9fT0lJCUVFRZSUlFBXV+e3b1hYWKN5KxuKiopqNMjfSsysrkwR0QRNKaU6oQMmXiISA9iANBFJBqx3+QSgx8EObIyZDcz2HGs8cJMx5hIR+QdwOXCv5+f/DiF+pTqU8PBwUlNTvfNU+s5RWV1djcvl8o4PsxbA231ZW1tLTU0NtbW1TSZuDYmINzGzZgHwbT3TMWdKKdWxNNfidQ0wC3eStYafE68y4JFDOOe9wCsi8htgF3DhIRxLqQ4tIiKiUWmLpjQcU2apr6/3Dvavra3FGNNosZK6srIyvyr+1vl9p1eKiIjw1j2zbvtu10RNKaWCSxq+UTfaQeR6Y8w/2ymeJo0ePdqsXr06lCEo1eEZY/xazJxOp/enNZ6svr6e+vr6Ax4jLCyM6OhobDYbcXFx3hIampAppVTgRGSNMWZ0U9sCGVzvEpEkY0yJ52DJwMXGmEfbMEal1CHy7XZsjjHGm4BZ815aP51OJzU1NZSUlLB//37vca0uUevx8PMVoFaCZrPZGhWctfbV8WhKKeUWSOI1wxjj7Vo0xhSLyAxAEy+lOiER8XY7HihJs1rPqqqqqKqqora21vtY66dVgLakpMT7uMjISG8XqMvl8iZeMTEx3qtC4+LiiI2N1WRMKdUlBZJ4hYmIGM87qGcKoKjghqWUCiXf1rPk5ORm962rq6OqqorKykpqamoQEcLCwrw/AW8RWt9WNOsCAN/F6uLUuTOVUoerQBKv93EPhv83YIBrgfeCGpVSqtOIiIhoNANAU6xWtMrKSiorK73jzyorK3E6nX4XBsTGxnovSoiJifFeCGAldEop1VkFknjdgvsKx5m4r2z8AHgqmEEppQ4/vq1oKSkpftuscWdVVVVUVFRQUVHB/v37KSgoaHQMq5vUd8qmqKgooqKiiI2N9RuPppRSHc1BEy9jjEtEFgCfGGM2BT8kpVRXYyVUvi1nxhjv+DLrQgDfxRqD1rDWWWRkpN+k5jabTSc2V0p1GIFUrp8M/AP3uK6+InIU8DdjzOQgx6aU6sJE5IDTNPlyuVzeqzGtSc0dDgf79u3zO5ZvMmYN8NcyGUqp9hZIV+NfgWOBZQDGmPUikh3EmJRSKmBW7bHo6Gi/cWYul4vq6mq/ZKy4uJjCwkLAnYz51iuLiorydmGGh4drC5lSKigCSbzqjDGl+iaklOpMwsLCvPXFrCmcfMtkWIP8CwoKGlX8B7xjyayB/b4lOKzpmXQ8mVKqpQJJvL4XkV8B4SIyEPg98GVww1JKqbbXVJkMYwzV1dXeQrK+RWWtpaamxjuezDdJi4iI8CZg1lRM1hIZGemdO1O7NJVSlkASr+uB24Ea4AXc5SXuCmZQSinVXqzxXweaL9OXMQan04nD4aC6utqvK9OaDaCp1jPfJMz6aS2alCnVtRww8RKR54wxl+KuXH877uRLKaW6LKvwa1RUFImJiU3u43K5qK+v986bWV1d7Z3ovLi4uNFcmVFRUd6aZfHx8XoFplKHueZavI4RkT7AlSLyH9w1vLyMMUVBjUwppTqhsLAwwsLCiIyMbPKKTKvr0lqqqqooKyujqMj9lhoREeGt3u87A0BYWFijumVa4V+pzqe5xOvfuCvU9wPW4J94Gc96pZRSLWAN0vdNyowx1NTUUFFRQXl5OQ6Hw9tt6XK5/Oa99GVNVG4tVrkMTciU6riaS7zeMsb8n4g8ZoyZ2W4RKaVUFyMi3isl09LSmtzHuiLT6XRSW1vrXRqWyQB3cme1ilmLNVF5REQgQ3uVUsHS3H/gYuAYYFA7xaKUUuoAfK/IbMh30L9V7b+2tpbq6mrKyspwuVzefaOjo72FabWQrFLtr7nEK0xE/goMEpE/NtxojHkweGEppZQKVHOD/q15MB0OBxUVFVRWVvqNKQN3MuY7xZLNZtMaZUoFSXOJ10XAOZ594tslGqWUUm3KmgczPj6e+Hj3W7lvIVmHw4HD4aCyspLi4mLv4yIiIrxJWGxsrLcrVFvHlDo0B0y8PBNi3yci3xpj3m3pgUUkBvgMiPacZ7Ex5q8iMgeYARR4dr3NGPNOiyNXSinVKk0VkgWor6+nqqrKm5BVVVX5zXkJ7vIX1mN9C8aGhYURHh7ubXmLiIjQshhKNaG5Ol7zjTGzjDHvisgNxpiHfbYtMMZccZBj1wCnGmMqRCQSWC4iVgL3kDFm3iFHr5RSqs2Eh4f7tYzBz3NeWvXIrNslJSUHLBgLeMtfREVFectiWImY1QrX8AIAnSNTdQXNdTWe5HP7cuBhn/sjD3Zg4/5vrPDcjfQsTf+HKqWU6pB857xsilXuwqrcbxWO9b3y0hrcb4zxLg2nX/I9n28LmjVxue8SERHht5/volRH11ziJQe4HTARCcddA2wA8IgxZqWI/BK4TkQuA1YDNxpjips7jlJKqY7JSnisMhUHStAaspIv3wTNSt7q6+u9yVxdXR0OhwOn03nQY1pzZFrJWcPbvuu0ZU2FysGuakwGwnxuW3+pAVXnM8bUA0eJSBLwhogMBx4D5uJu/ZoLPABc2fCxInI1cDVA7969A3oySimlOgcR8SZBTVX4b8hK1KwJzK2WNt8WN6fT6V2qqqpwOp1+pTR8z23Nm2nNnWlNdG4VuNVuTxUscqD+eRHZAbhourXLGGNaVLneU5qi0ndsl4hkA0uMMcObe+zo0aPN6tWrW3I6pZRSCpfL5U3WrKSs4RyaB/ocjIiIIDo6utFYNGvaJr2AQB2IiKwxxoxualtzVzVmH+JJ0wGnMaZERGKB03BfJdndGJPr2e1c4PtDOY9SSil1IGFhYQcsPAs/l9aoq6vzLlYXp9UFWlVVRUlJSaMEzbfVzmops25bhWq1HppqKJhzR3QHFnrGeYUBrxhjlojIcyJyFO6uxh3ANUGMQSmllDqg5mYE8OU7Js2atqnhT6t701d0dDR2ux273e6dR9P3YgDfqz1V1xC0xMsY8y0wqon1lwbrnEoppVQw+LZuNceaKaC6upqKigoqKiooKSlh//79Bzyub200q2uzYXJmlefQKzc7P50tVSmllGojVo0yq5UL3MmYNa6s4QUBviU4Kisrqa+vb/bY0dHRxMbGehcrUQsPD+iaN9UBBJR4iciJwEBjzLOesVt2Y8z24IamlFJKdX4i4r2C8mCs7kwrOTPGeG9XV1c3Ob0T4DdrgHUua6onTco6loMmXp6rEUcDg4FncRdCfR44IbihKaWUUl2LNUj/YKzuTN9itdZVmmVlZX4XAvhejWkd37oQwCqnoV2Y7SeQFq9zcY/VWgtgjNkrIjpptlJKKRUi4eHhxMXFNVkDzeradDgc3lYya/C/ddVmQ1Zds+joaL/kzLforDXeTB2aQBKvWmOMEREDICIHr3SnlFJKqZA4WNem7xWaDefgLC8vb7LoLLhLc/hO3dTUlE2+0z35TpyuBWl/Fkji9YqIPA4kicgM3FXmnwxuWKqtVFVV8dZbb/Hmm2/icDi832isn+Xl5RQUFJCfn09BQQGFhYUcf/zxPPnkk/Ts2TPU4SullGpjB5s1wOVy+dU18y2j4TszgHWBwIESNV++9dSsmQKsGQJ8f3aForQHTbyMMfNE5HSgDPc4r78YYz4MemQh9uOPP/L0009zxx13kJiYGOpwWqS2tpYPPviAF198kf/9739UVlbSrVs30tPTG327sdvtpKenk5GRQf/+/YmPj+f5559nxIgRPProo1x88cWhfjpKKaXakVW6IioqKqD9rYnPfa/WbOqqTav7s7S09ICzBQB+SVjDCdIjIyO9yVtnTdACGVz/B+DVrpBsWZYuXcp5551HSUkJRUVFPP3006EOKWCvvPIKv/vd7ygsLCQlJYXp06dz8cUXM27cuICvbPnTn/7EpZdeyq9+9SvefPNNHn30UZKTk4McuVKh53A42LJlC5s3b2bHjh1kZGQwZMgQBg8eTEJCQrOPdTqdbN++nU2bNrFp0yby8vKoqqqisrKSqqoqqqqqqK+v9ysFEBsbS1hYGKWlpRQXF1NSUkJxcTEVFRXeaWmsJSIiwu/DzbriLTU1lW7dutG9e3e6d+9Ot27dvIU6rZaE8PBwYmNjvSUO4uLisNvtRERENCoEGhERQXJy8iFVXHc6neTl5bF3717y8vIIDw/HZrP5Pe/w8HDvB7b1IRwTE0NCQgJ2u12vxOtErCKwgQ7Qt2qdWTMEWD+bWqzuz4bj0sLCwoiNjcVms3n/tjrLFZwHnKvRu4P7qsapQBHwErDYGJPXDrF5tedcjQsXLmTGjBkMHDiQ448/nqeeeop33nmHX/7yl+1y/taqrKxk1qxZPPXUU4wZM4Y///nPnH766QF/Y2morq6O++67jzlz5pCZmcn//d//cfbZZ3ea6S+MMTidTsrLyyksLGT//v3enzU1NfTt25eBAwfSu3fvgK4g8j1uZ/2WFYjKykpKS0u9XdHWQFtrWpXKykoqKyupqKhARMjOzg7oEvm2ZL1ntcXrYIxhx44drFu3jk2bNrFz506MMURERJCVlUV+fj4OhwOA+Ph4YmNjvQOXy8rKKC0tpaSkhB07drB161bq6uq8x46JifEOfrbZbMTFxREWFobD4cDhcFBVVYXD4cDlcpGUlORdkpOTiYuL87YU+CZF1oebtRhj2L9/P/v27WPfvn1+5z9U8fHxpKSkkJKSQkJCgneMjnVuwPvhaM2FWF1dzb59+ygoKGi2RSMQdrudhIQEbDab92/R+rv0vUrP6rISEW+LilVywel0kp6eTrdu3cjMzKRbt25kZGR4P6QbHtM6nnW7qSKmVr2tiooK7/9DU4sxxpvoWsmu73OxiqY2lVBbVyxaA+Ot21ZLkrW/McYvobaWhkmt7/6+S1RUFMnJyYecaLcHa85Na65N68uM1eVpiYiI8HttreSsvZ9fc3M1HjTx8jnISGAacD6wxxhzWtuF2Lz2SLzGjx/Pjh072LlzJ0lJSQwbNoypU6fy+OOPU1RURP/+/Rt9QF9xxRVcccUVFBYWcsEFFzQ65syZM5k2bRq7d+/m0ksbF+w/++yz+frrr9m9ezeFhYWkp6f7/XHccccdnHbaaaxfv55Zs2Y1evzdd9/N8ccfz8KFC5k5cyYOh4PevXuTnZ2NiDB//nyOOuooPvroI+66665Gj3/88ccZPHgwb731Fg888ECj7c899xz5+flMnjyZvXv3EhkZSUZGBt26dcNut7N48WLS0tJYsGABCxYsaPT4d955B5vNxqOPPsorr7zSaPuyZcsAmDdvHkuWLPHbFhERwfz589m7dy/PPPMM3377rd+3/KioKCZMmEBBQQFfffUVhYWF1NXVtWjMgXUem83WaOBnQkICQ4cOpby8nO+++w6Hw+H9ZhYeHk5iYiIjR46ke/furFq1yjvRrvX/lJWVxbhx40hJSWHRokUYY7yDUUWE8ePHM2PGDKKiopg+fbq3VcKKYerUqcycOZPCwkKmTJni9+HmdDo58sgjyc7OZt++fXz00UeNBrSOHz+eMWPGUFpaylNPPQXg9+ExdepUTjrpJFavXs3DDz/s/bCorq4O6Pfmq2FBx/DwcKZPn87gwYPZtGkTr732mt+Hisvl4vzzzycyMpI1a9awatUq7/Oy4jzyyCNJSkqioKCAn376yfuGa+0XHh5OWloa4eHhVFZW+g32DQ8P59prryUtLY3ly5ezcuVK4OeEzeVycckll1BUVMSKFSvYtWuXd731N5SZmUl5eTn79u3zdrtYH5YxMTGcccYZ1NbWev/2wsLCiImJwWazkZ2dzQsvvEBKSgqzZs1i/fr1fr+vQYMG8cQTTwBw9dVXs3nzZr/tRx11FPPnzwfgkksuYc+ePX7bx44dyz333APA+eef71cR3el0cvTRR3PFFVdQV1fHrFmzqK6u9n7w1tfXM2zYME488UTKy8t56qmnvH8T1s+jjjqKESNGsG/fPhYvXozT6aS+vt77+0tPTyctLY3a2lq2bt3qbe3wffy4ceOIjo5m0aJFREVF+SUWEydOZOjQoezdu7fR+4bL5WL8+PFkZGSwbds2PvnkE7//KxHhmGOOoWfPnuzbt49Vq1Y1+nscO3YsaWlp7Nmzh3Xr1jVKPIYPH050dDS5ubneRNt36datGwClpaWUlZX5/e0YY7DZbN4kr7a21nteax8rKW2uEGpHFBYWhs1mo1evXoSHh7Nnzx6/RN56D7Pb7d7uQsBvgH1ycjL9+vUjKiqKb775BpfL5dcK1r17dwYPHgy43/99/3asL3IDBw7E4XCwdOlSv9ddROjbty8DBgzA6XTy2Wefed8vrS7JU045hQkTJlBbW8vDDz/sd26Xy8WkSZMYOHAgffv2Zdy4cUH9fbZqkuwm5AP7gP1ARlsE1lHU1NSwceNG8vPz6datG4MGDfJWH16wYAHHHXccxhiGDBkS8DGdTmeTk6oCFBUVsWvXLj799FMSExNJTk5mx44d/PTTTyQnJ5ORkUFiYiIbN26kpqaGNWvWsHv3burr6/0u8V2zZg0rVqzglltuISwsjJEjR7Z5l+AxxxzD/fffz7333su+ffvYu3cvOTk52Gw2HnvssSYTwubU19ezc+dOcnJyvN/OrG/K4eHh3m8zLpeLESNGNHusvXv3kp6eTl1dHTExMURERHiTj8TERC6++GLsdjvvvvuuN3GMjIxEREhPT+ecc85hy5YtvPTSSxQWFvq9VpWVleTl5REfH4/dbve7xLqurg673Y7T6WTlypXs3LkTl8vlN+daUVER33//PVVVVU3GvnbtWh588MEmt4WHh7N69WpuuOGGA7ZgbNq0iaioKBITEykuLvb7YATYsmWLN+Fqynfffed332azER8fT7du3YiMjOT000+nT58+7Nixg7ffftsbl/X7nT59Ov379+eTTz5hyZIlOBwO8vPzvR82c+bMOeC5Ae69915EBJvNRn19vbeVAdxvkFaLQl5eHtXV1d43fOsN9txzz8XhcLBmzRq2bNninSPPSrpnz57td76GyVNOTg4ul4vy8nIqKyu9HxDh4eFERkZy5JFHYrPZ2LJlC7m5uX6tLImJiUyfPp2dO3eydetW74dzXV0dVVVVFBcXs2bNGnr27InD4WjXVlLry9ExxxwDQFJSkrfFznLsscfy+9//HoAPP2w8guTkk0/mt7/9LVVVVXz//feNth/sC+eMGTO8Xzjfe+8973qra6lXr14MHDgQp9NJWFhYoy6nvXv3AlBdXe33P2X9/x599NEce+yx7Nixgz179vh9aXG5XFx00UX07NmTzz//3JtY+bYkjRgxgoSEBDZs2MD+/fv9EjuAMWPGYLfb2bp1Kxs2bGj0/E4//XRiYmLYtGlTo6QZ4Je//CURERH88MMPbNu2rdH2c845h7CwMNatW8eOHTv8/jYiIiI455xzEBG+/vprdu3a5fc7sNlsnH/++YB7SIyVlFvx2+12zjzzTIwxLFu2jIKCAr9zJycnc9pp7jaTjz76iOLiYr+kMjU1leOOO857/MrKSr/HZ2ZmcuyxxyIifPDBB9TU1Pht79atm/dzctOmTY3ev2JjY72fUU31NFhfYKz/84as1r3q6mq/pMr6G9q5cyeffvqp973D9yICq2V0yJAhbN68OeiJV3MC6WqcibulKx1YDLxsjGn81xhEwW7xmjNnDnfeeSd33XUXt912W6M3ydtvv527776bJUuWMHHixGaPZYzhX//6FzfffDPV1dXExcXRr18/+vfvT9++ffn444/59ttvycrK4g9/+ANXX301drudb7/9lpdeeomXX36Z7dtbNinAxIkTefbZZ0lPT2/xc2+poqIiXn75ZRYuXMjKlStJTk7muuuu4/rrr2/2/HV1dTz11FP85S9/oaCggKlTp9KrVy8qKiooLy/3NtunpKTQs2dPsrKyvD8TExP9PjSjo6OJj49vdTdqe6qurqa4uJji4mKKioqoqKhoNLFudXV1o26Kuro6kpKSSExM9PuZlpbmXeLi4vz+Vl0ul7cLy0pCfBfrfNY39ZqaGu8YpoNNEBwIYwzl5eVUVVV5u0gcDgc1NTXeZn/fitpW91Vbq6urY9u2bWzYsIHt27eTk5NDeXk54G6d69WrF8cccwzHHnusd0qXQ+F0Otm9ezfbtm1j+/btbN++3a8VKiwszPuaJScne7u5fFsJExMTSUxMJCEhocP9XTecHNr6O7L+dn27wqwuPmuOQmspKytrNHk0uD984+PjiY+PJyEhgYSEBO/vwfqdJCcnk5SUFPSxO1bXrnUBUk1Njbcr1XcMUlMDyBt2E1pjmBq2tjUcdO7bdeibAPqu8+1ahJ9b1HwTMt/Pcd9Ev6l9G36+NZys27cF1HfcVsMuV99u54bd0A2Pd6CyE9bi21rf8BzW7aaO4XvOpp5jU8+nYctksBxSV6OI3Au8ZIxZH4TYAhLsxKuyspKlS5cyadKkJrfX1NQwevRo9u/fzw8//HDAVqXc3Fx+/etf8/777zNx4kTOPPNMtm7d6l22bdtG//79uemmm/jVr37V5BusMYZVq1bx448/kpqaSlpamrdpPy4ujvLyckpKSrxLWFgY48aNC8m4o6+//pp7772XN954g9jYWGbMmME111yD3W73+xb1/fffc8stt7BhwwbGjRvHgw8+yOjRTf49KtViTqeTnJwctm3bxk8//cRPP/3kTbQSEhIYOHAgAwYMYODAgWRlZbVLhe7S0lLvWCdrKSwspLS01JuMHkhsbKz3i4XvlV3W2JWGS8MPL6vlp+H4K99SAA1LA/hubziuzOl0tmi8VkxMjN8A/ri4OG8SZX2JsJKrmJiYw3rMpOq6WpV4iUiCMaZMRFKa2m6MKWrDGJvVnoPrD2TNmjWMGTOG6dOns3Dhwkbb//vf/3LVVVdRVVXFgw8+yDXXXNPoDeVwHZi9ceNG7rvvPhYtWnTArrEBAwZw//33e5vRlWoNa/D2nj172Llzp7fb2vq7S01NZeDAgQwcOJBBgwaRnp7eIf/eGs67Zw3UtxarZdRKiqzEyCoF43A4mmxBao5V/NJK6HwHk1uJne/9hgPYfe9bt61Jmq1WPKubSKmurrWJ1xJjzCQR2Q4YwPfdyxhj+rV9qE3rCIkXwJ///GfuuusuUlJSvLWvMjIyqK2t5a233uLoo49m0aJFLRoLdjjZtWsXH330kTfBtJb4+HjOPvvsDteFojomYwzFxcXk5uaSm5tLXl4e+/btIy8vzzugF9wtQ71796ZPnz5kZ2eTnZ1NampqCCNvX/X19dTU1DTq8rIuAGk4L19nuMxeqcNFm1zVGEodJfGqra3lscce46effiI/P99b7b2kpITLL7+cOXPmaHKhVADq6+spKipi//79fsu+ffvIzc3164qLi4sjMzPTWw4gMzOTHj16kJ6erhP7KqU6pEMd4/WxMWbCwdYFU0dJvJRSgXO5XBQWFpKTk+P9kmItRUVFfuOGRISkpCQyMzO9hUCtJT4+PoTPQimlWq5V5SREJAawAWkikszPXY0JQI82j1Ip1elYJRmsmkdFRUXs2bPHu/i2XFnTU/Xv35/jjjvOe/FIamoqycnJ2hWmlOoSmhsFeQ0wC3eStYafE68y4JHghtX+DteB70q1FZfLxZ49e7xT4uzatYuysrJGV7zFxMTQs2dPjj/+eHr27EnPnj3JzMwkNjY2RJErpVTHccDEyxjzMPCwiFxvjPlnSw/saTH7DIj2nGexMeavnqskXwaygR3AVGNMcStibzNffPEFb7/9NnfeeWeHnzZBqfZSWVnJ7t272bVrF1u3bmXz5s3egrCZmZkMHTqU5ORkv7pL1vQj+iVGKaWadtDrfo0x/xSR4cBQIMZn/X8O8tAa4FRjTIWIRALLReRd4DzgY2PMvSJyK3ArcEurn0EbSExMZP/+/WzcuJGRI0eGMhSl2p3T6SQ/P987sD0nJ4ddu3ZRWFjo3SctLY1Ro0YxePBgBg0apJOmK6VUKx008fJMkj0ed+L1DvBLYDnQbOJl3P0PFZ67kZ7FAFM8xwNYCCwjxInXkCFDsNlsrF27VhMvFTJ1dXXk5eWRk5NDWVmZ9yq+1NRUv/nf9uzZw+bNm/npp5/YtWsX0dHR3umXrCmOGtZgioyMpLq62jtLgPXTKuzpOydaWloaffr0Ydy4cfTu3ZvevXu3SYV3pZRSgc3VeAFwJLDOGPNrEckEDjwJnA8RCcc9PmwA8IgxZqWIZBpjcgGMMbki0uS8jyJyNXA1QO/evQM5XatFRERw5JFH8s0331BXV6cFAFWr1dfXs2rVKj788ENKS0ux2WzYbDbi4uKw2WxERUX51TgDqKqqIicnh3379jU5uXdkZCSZmZnExcWxc+dO70TW6enpDBw4kLq6OioqKsjPz2fr1q1UVFQ0W2ncmnLJbrfTu3dvjj32WLp37+4t1aAlUZRSKngCyTAcxhiXiNSJSALuybIDKp5qjKkHjhKRJOANT5dlQIwxTwBPgLucRKCPa62jjz6ar776ih9//JHhwwMOUynA3V335Zdf8sEHH1BYWEiPHj0YNWoUlZWVVFVVUVZWxr59+6itrQXwm5stJiaGHj16MHLkSLKyssjKyiI+Pt7b/WctZWVlHHvssd7K7Afq7rPm1ms4RYw1lYsmVkopFTqBJF6rPYnTk7hbryqAr1tyEmNMiYgsA84E8kSku6e1qzvuRC7kjjjiCGJiYli7dq0mXipgDoeDzz//nA8//JCysjL69u3L1KlTGTFixCEX90xISGDAgAEtfpyIeLsXlVJKdSyBDK7/refmv0XkPSDBGPPtwR4nIumA05N0xQKnAfcBbwKXA/d6fv6vtcG3pcjISEaOHMn69euZPn261hRSzSouLuaTTz7hs88+o7q6msGDB/Ob3/yGwYMH6xV9SnVCZWVl5Ofnt3gOTNX1REZGkpGRQUJCQqse31wB1aOb22aMWXuQY3cHFnrGeYUBrxhjlojIV8ArIvIbYBdwYSviDopjjjmGr7/+mk2bNjF06NBQh6M6oJycHD744AO+/vprjDGMHj2a0047jezs7FCHppRqpbKyMvLy8sjKyiI2Nla/PKkDMsbgcDjIyckBaFXy1VyL1wPNnRs49SDBfQuMamL9fqDdphtqiaFDhxIdHc3atWs18VJ+9u/fz//+9z9WrlxJVFQU48ePZ8KECaSlpYU6NKXUIcrPzycrKwubzRbqUFQHJyLYbDaysrLYu3dv2yZexphTDim6TigqKsrb3XjxxRdrd6OisrKSd999l6VLlyIinHnmmZxxxhnExcWFOjSlVBtxOp06s4JqkdjY2FZ3SwdSx+uyptYHUEC1Uzr66KNZtWoVW7ZsYfDgwaEOR4WI0+lk2bJlvPPOOzgcDo477jimTJmihUOVOkxp96JqiUP5ewnkqsZf+NyOwd1NuJaDFFDtrIYPH05UVBRr1qzRxKsLcrlcrFy5kjfffJOioiKGDRvGeeedR8+ePUMdmlJKqcNAIFc1Xu97X0QSgeeCFlGIRUVFMXz4cNatW8dFF110yCUBVOdgjOH777/n9ddfZ+/evfTu3ZvLLruMI444ItShKaWUOoy0JquoAga2dSAdydFHH01ZWRlbt24NdSgqyIwx/PjjjzzwwAP861//wul0MmPGDGbPnq1Jl1JKecybN69LXb1tt9tZsGBBUI4dyBivt3BfxQjuRG0o8EpQoukgRowYQWRkJGvXrmXgwMM6x+yyXC4X69at4/3332fnzp0kJCRw8cUXc+KJJ+qUUUoppYImkE+YeT6364Cdxpg9QYqnQ4iJiWHYsGGsXbuWCy+8ULsbDyNOp5OvvvqKDz/8kPz8fDIyMpg+fTpjx47VSu9KqU6ttrZWpwTz4XQ6O+T7+kEzCmPMp8aYT4F1wEagSkRSgh5ZiI0aNYqSkhJvkTTVuVVUVPD2228ze/ZsFi1ahM1m45prruHOO+/kpJNO6pD/nEop1Zzx48czc+ZMbrrpJtLT0znhhBN48MEHGTlyJHFxcWRlZXHVVVdRUlLifcyCBQuw2+18/PHHDB8+nLi4OE455RS2b9/ud+z777+fbt26Ybfbueyyy6ioqAg4riuuuIJJkyZx33330a1bNxITE7n11ltxuVzMmTOHjIwMunXrxn333RfwMUWEf/3rX0ycOBGbzUafPn14/vnnvdt37NiBiPDiiy9y6qmnEhsby+OPPw7As88+y9ChQ4mJiWHQoEE89NBDuFwu72O3bNnC+PHjiYmJYfDgwSxZsiTguFojkK7Gq4G5gANwAYK76zGgibI7qx49egBQUFBAr169QhyNaq2CggI++ugjvvjiC5xOJ8OHD+eMM85g0KBBevm4UuqAZs2axfr169v1nEcddRTz589v0WOef/55rr76aj7//HOMMbz//vvMnz+ffv36sXPnTq6//nquv/56nnvu52viampquOeee3jmmWeIiYnh8ssv59prr+X9998H4JVXXuGOO+7gn//8J6eccgqvvvoq9913Hykpgbe5fPbZZ/Ts2ZNly5axbt06pk+fzvr16xk1ahTLly/nk08+YebMmZx22mkcc8wxAR3zr3/9K3fffTcPPfQQr776KpdddhlDhgxh9OjR3n1mz57NvHnzePrpp4mMjOTJJ5/kL3/5C//85z855phj+P7775kxYwaRkZFcd911uFwuzj33XJKTk/nqq6+oqqrihhtuoKamJuDn2lKBdDX+CRhmjCkMWhQdUGpqKuCuWK46n4KCAt58801WrVpFWFgYY8aM4fTTT/cm1EopdTjo27cvDzzw80QzvhcFZWdnc//99zNlyhQWLlzoHTZTV1fHI4884i2ZdNNNN/HrX/8al8tFWFgY8+fP5/LLL+eaa64B4Pbbb2fp0qVs2bIl4LgSExN55JFHCA8PZ8iQITzwwAPs3buX9957D4BBgwZx7733snTp0oATr/POO69RTPPnz/dr+br++uu54IILvPfnzp3L/fff713Xt29fbr31Vh599FGuu+46PvroIzZs2MD27dvp3bs3APPnz2fcuHEBP9eWCiTx2or7SsYuxWazERMTo4lXJ1NSUsLbb7/N8uXLCQ8P5/TTT2fChAkkJSWFOjSlVCfS0panUGmYtHzyySfcc889bNy4kdLSUurr66mtrWXfvn3eL57R0dF+dSp79OiB0+mkpKSElJQUNm7cyFVXXeV33LFjx7Yo8Ro6dKjf7C+ZmZmN3oczMzPJz88P+Jhjx45tdP/tt9/2W+fb+lVQUMDu3bu55pprmDlzpnd9XV0dxrivGdy4cSNZWVnepAtgzJgxQR3bHUjiNRv4UkRWAt62N2PM74MWVQcgIqSlpVFY2KUa+jqtyspK3nvvPZYuXUp9fT3jxo1j4sSJJCYmhjo0pZQKGt/py3bu3MnEiROZMWMGf/vb30hNTWXt2rVcfPHF1NbWevdreOW2NezCd9zToWo4blZEmlzXlucE/9+Hdex///vfHH/88U3ubyVg7SmQxOtx4BPgO9xjvLqM1NRUCgoKQh2GakZdXR3Lli3j7bffxuFwMGbMGCZNmkR6enqoQ1NKqXa1evVqamtreeihh7ytTa0ZKH7EEUewYsUKrrzySu+6FStWtFmcrdVUTM3VW8zMzCQrK4utW7dy2WVNzn7I0KFDycnJYffu3d7x3F9//XWbJ4S+Akm86owxfwxaBB1YamoqP/74I8YYHYjdwRhj+Oabb3jttdfIz89n6NChXHDBBWRlZYU6NKWUComBAwficrmYP38+5513HitWrGhVl+kNN9zAZZddxi9+8QvGjx/P4sWLWblyZYsG1wfD66+/7hfTxx9/zMqVK5t9zJw5c7j++utJSkrirLPOwul0snbtWnJycpg9ezannXYaQ4YM4bLLLuOhhx7C4XDwhz/8Iaj1HAM58lLPlY1v4d/VWBS0qDqI1NRUampqqKysxG63hzqcLs0YQ1VVFSUlJezfv58PP/yQzZs30717d66//nqGDx8e6hCVUiqkRo4cycMPP8x9993HHXfcwfHHH8+8efOYNm1ai44zbdo0tm3bxu23305VVRWTJ0/mj3/8Y9AquQdqzpw5vPbaa/z+978nPT2dZ599ll/84hfNPuaqq64iLi6Of/zjH8yePZvY2FiGDRvGddddB0BYWBhvvPEGM2bMYMyYMfTu3ZsHHniAX/3qV0F7HnKw/k0R2d7EamOMabdyEqNHjzarV69ur9N5rV+/nscee4zZs2d3qakSQqG+vp4NGzZQWFhIeXk55eXllJWVUV5eTmlpKSUlJdTV1Xn3t9vtTJ48mRNPPNFvAKdSSrXUxo0bdYqwDk5EePXVV/2uWAy15v5uRGSNMWZ0U9sCmSS77yHG1mn5lpTQxCs4KisrWb58OUuXLqW4uBhw/4PZ7Xbi4+OJj4+nX79+JCUlkZiY6P3Zq1cvYmJiQhy9Ukop1TKBFFBtckSaMeY/bR9Ox6K1vIInLy+PTz75hC+//JLa2loGDx7MxRdfTL9+/YiLi9NpmpRSqoNqbujNu+++2+IaWIsWLfLW52qoT58+/PDDDy06XkcXyBgv3w7UGGACsBY47BMvm82GzWbTxKsN1dfX88477/D2228THh7OL37xCyZMmKCzAyilVCfRXEX/1lzgNHnyZMaMGdPkNqsERSjKPgRLIF2N1/veF5FE4LkD7O67Xy/cyVk33GUonjDGPCwic4AZgFWn4TZjzDstjLvdpKamai2vNlJUVMTTTz/Nli1bOO644zjvvPO0zpZSSnUyAwYMaNPjWcNKuorWXC9ZBQwMYL864EZjzFoRiQfWiMiHnm0PGWPmteLc7S41NZW8vLxQh9HprV27lueee476+nquvPLKA367UUoppQ5ngYzxegv3pNgAYcBQ4JWDPc4Ykwvkem6Xi8hGoNMVWUpNTWXDhg1ay6sVqquryc3N5csvv+Szzz4jOzubq666SoubKqWU6rICafHybZmqA3YaY/a05CQikg2MAlYCJwDXeQbtr8bdKlbcxGOuBq4G/OZQam9paWnU1tZSUVHRpZpCW6OgoIDly5eTk5PD3r17/cbGnXHGGUyZMiWoRemUUkqpju6An4IiMgDINMZ82mD9OBGJNsZsDeQEImIHXgNmGWPKROQxYC7uVrS5wAPAlQ0fZ4x5AngC3HW8Anw+bc66srGwsFATr2asWrWK559/HqfTSWZmJv369eOEE04gKyuLnj17kpaWFuoQlVJKqZBrrvlhPnBbE+sdnm1nH+zgIhKJO+laZIx5HcAYk+ez/Umg5RNJtSMrYdi/fz99+3bZkmYHVFtby8svv8zy5cvp168fM2bMCPm0EkoppVRH1VyxpGxjzLcNVxpjVgPZBzuwuAdEPQ1sNMY86LO+u89u5wLfBxxtCFhJhJaUaGzv3r3cc889LF++nDPPPJObbrpJky6llOrARITFixeHOoxGCgsLERGWLVsW6lCCrrkWr+bKgscGcOwTgEuB70RkvWfdbcDFInIU7q7GHUDTVdM6iNjYWOLi4jTx8lFUVMQXX3zB+++/T0xMDL///e8ZNmxYqMNSSimlOrzmEq9VIjLDGPOk70oR+Q2w5mAHNsYsB5q6DLDD1uw6EK3lBU6nk2+//Zbly5ezceNGjDGMGDGCSy+9VGtxKaWUAtyfFVbRU9W05roaZwG/FpFlIvKAZ/kUuAq4oV2i6yDS0tI6TYuXy+Vi69at5Obm+k0q3Zrj5OTksHz5cv7zn/9w66238sQTT5Cbm8tZZ53F3//+d6677jpNupRSKkTGjx/PzJkzufHGG0lJSSE9PZ2HH36Ympoafve735GUlETv3r157rmD1jxvZMeOHYgIL7zwAieeeCIxMTEMGTKEDz74wLvPsmXLEBHeeecdjj32WKKionj//fcxxnD//ffTv39/YmNjGTFiBM8//7zf8VetWsUxxxxDTEwMo0aNYuXKlYf8++gsDtji5RkEf7yInAIM96x+2xjzSbtE1oGkpqby3XffdfhaXps3b+bVV19l165dgLsvPy0tjczMTDIzMxk4cCBHHHFEk5NLG2PYvXs333zzDVu2bGHHjh1UV1cDEBcXx5AhQzj++OMZOnSozqOolDrsvfzyy+zZ06LKSYesZ8+eTJs2rUWPWbRoEX/84x9ZuXIlb775JrNmzeK9997jzDPPZPXq1SxcuJCrrrqKCRMm0KNHjxbHdPPNN/Pggw8ycuRIHnnkEaZMmcKWLVv8pga65ZZbeOCBBxgwYADx8fHccccdLF68mEceeYTBgwfz1VdfMWPGDJKTk5k4cSKVlZVMnDiRk08+mYULF5KTk8OsWbNaHFtnFciUQUuBpe0QS4eVmpqK0+mkvLychISEUIfTSEFBAa+99hrr1q0jOTmZSy+9lIiICPLz89m3bx/5+fls2rSJjz/+mIiICAYOHMiIESMYNmwYxcXFrF+/nm+//ZaioiJEhF69enHcccfRt29f+vbtS0ZGRodOOJVSqqsaNmwYc+bMAeCPf/wj9957L5GRkdxwg7tj6i9/+Qv33XcfX375JRdccEGLjz9z5kymTp0KwMMPP8z777/PY489xl133eXdZ86cOZxxxhkAVFZW8uCDD/LBBx94J8vu27cvX3/9NY888ggTJ05k0aJF1NbW8uyzz2K32xk+fDi33347l1566aH8KjoNrWYZAKuW1/79+ztU4lVTU8Nbb73F0qVLCQ8PZ/LkyZx++ulERUU12re+vp4tW7bw3Xff8d133/HKKz9PPhAZGcnQoUOZNGkSI0eO1HplSqkur6UtT6EycuRI720RISMjgxEjRnjXRUZGkpycTH5+fquOP3bsWO/tsLAwxowZw4YNG/z2GT16tPf2hg0bqK6u5swzz/T7wu50OsnOzgZg48aNjBw5Ervd3uR5DneaeAXAquVVWFjYYWp57dmzhyeffJK8vDzGjh3LlClTSEpKOuD+4eHhDB48mMGDB3PBBRdQUFDAhg0bSEpK4ogjjmgyWVNKKdWxNRzILiJNrnO5XEGLIS4uznvbOs9bb73VaNYZKy5jQlYTvUPQxCsAHamWlzGGzz77jFdeeYW4uDj+8Ic/MHjw4BYfJz09nZNPPjkIESqllDpcrFixglNPPRVwf/58/fXXzXZZDh06lOjoaHbu3Ol9XFP7LFy4kMrKSm/StmLFirYPvoPSxCsAMTEx2O32kCdeDoeD5557jjVr1jB06FB+/etfd6iuT6WUUoeXxx57jEGDBjFixAgeffRRdu7cycyZMw+4f3x8PDfddBM33XQTxhhOOukkKioqWLFiBWFhYVx99dX86le/4vbbb+fKK6/kL3/5C3v37uXvf/97Oz6r0NLEK0ChrOVljGHjxo0sWrSIoqIizjvvPE4//XS9ulAppVRQ3XvvvTz44IOsXbuWPn368MYbb9CzZ89mHzN37lwyMzOZN28eM2fOJCEhgaOOOoqbb74ZALvdzpIlS5g5cyZHH300Q4YM4b777mPy5Mnt8ZRCThOvAKWlpbX7pcUAP/30E//973/ZsmULaWlp3HTTTfTv37/d41BKKdWxNDW9zvffN56Fb9++fd7bLR1fNXjwYL788ssmt40fP77J44kI119/Pddff/0BjztmzBjWrl3rt66rjP3SxCtAqampfPPNN7hcrnZpadqxYwf/+9//2LBhAwkJCVx00UWceOKJWhFYKaWU6sQ08QpQamoqdXV1lJeXB71a+4cffsjixYuJi4vjvPPO45RTTtGrDpVSSrWZu+++m7vvvrvJbePGjeOxxx5r54i6Dk28AmTV8iosLAxq4lVaWspbb73F8OHDueqqq4iNDWQ+cqWUUipw1157rbcwakOxsbFkZWV1ma6/9qaJV4CsWl779+8P6hirJUuW4HQ6mTZtmiZdSimlgiIlJcVbKkm1L70sLkC+LV7BkpeXx/LlyznppJPIyMgI2nmUUkopFRqaeAUoKiqK+Pj4oNby+u9//0tkZCQTJ04M2jmUUkopFTqaeLVAampq0BKvbdu2sXbtWs444wwtiqqUUkodpjTxaoG0tLSgJF7GGF577TUSEhI47bTT2vz4SimllOoYNPFqAavFq60nG/3222/ZsmULkyZNIiYmpk2PrZRSSqmOQxOvFkhNTaW+vp7S0tI2O2Z9fT1vvPEGmZmZnHjiiW12XKWUUupwtnjxYkQk1GG0WNASLxHpJSJLRWSjiPwgIjd41qeIyIci8pPnZ3KwYmhrviUl2sqKFSvIzc3lnHPOITw8vM2Oq5RSSh3InDlzGD58eKjD6JKC2eJVB9xojDkCOA74nYgMBW4FPjbGDAQ+9tzvFKzEq6CgoE2OV1dXx5IlS8jOzmbUqFFtckyllFKqs6irq+tyhVqDlngZY3KNMWs9t8uBjUAWMAVY6NltIXBOsGJoa2lpaYSFhZGXl9cmx1uxYgVFRUWcffbZnbK5VCmlVOgYY3jggQcYOHAg0dHR9OzZk9mzZwNw6623MnjwYGJjY8nOzubmm2+muroagAULFnDnnXfyww8/ICKICAsWLADcs6dcffXVZGRkEB8fz8knn8zq1asDimfBggXY7XbeeustBg0aRExMDKeccgrbtm3z7mO1tC1YsID+/fsTHR1NZWVlQOf9z3/+Q58+fbDZbEyaNKnNPovbW7tUrheRbGAUsBLINMbkgjs5E5EmK4WKyNXA1QC9e/dujzAPKjw8nLS0NPLz8w/5WPX19bz77rtkZ2czbNiwNohOKaVUW9m9ezdVVVXtek6bzUavXr0C3v+2227jscce48EHH+Skk06ioKCAdevWARAXF8czzzxDVlYWGzZs4NprryU6Opq5c+cybdo0vv/+e5YsWcKyZcsASExMxBjDxIkTSUxMZMmSJaSkpLBw4UJOPfVUNm3aRPfu3Q8aU01NDXfeeSfPPvssNpuNG264gXPPPZf169d7Gxi2b9/OCy+8wKuvvkpUVBTR0dGccsopzZ535cqVXHHFFcydO5cLL7yQpUuXctttt7X8l9wBBD3xEhE78BowyxhTFmjLjjHmCeAJgNGjR3eYdsiMjIw2Sby+/vprCgsLmTp1qrZ2KaWUapGKigoeeugh5s+fz5VXXgnAgAEDGDt2LAB//vOfvftmZ2dz2223MW/ePObOnUtsbCx2u52IiAi6devm3e+TTz5h/fr1FBQUeKesmzt3Lm+99RbPPfccN99880Hjqqur4+GHH+aEE04A4LnnnqNfv358/PHH3nJJtbW1PPfcc2RmZgZ83ocffpgJEyZw++23AzBo0CBWrVrF008/fUi/x1AIauIlIpG4k65FxpjXPavzRKS7p7WrO3DoWUw7yszMZPPmzRhjWp0w1dfX884779CrVy9GjhzZxhEqpZQ6VC1peQqFDRs2UFNTw4QJE5rcvnjxYubPn8+WLVuoqKigvr6e+vr6Zo+5Zs0aqqqqSE9P91tfXV3N1q1bA4orLCyMY4891nu/T58+9OjRgw0bNngTr549e3qTrkDPu3HjRs4++2y/7WPHjtXEy5e4s5KngY3GmAd9Nr0JXA7c6/n5v2DFEAyZmZnU1tZSUlJCcnLrLshcvXo1+fn5XHvttdrapZRSqsWaG5C+YsUKLrroIv7617/y0EMPkZSUxJtvvslNN93U7DFdLheZmZl8/vnnjba15YwqcXFxLT7v4TQAP5gtXicAlwLfich6z7rbcCdcr4jIb4BdwIVBjKHNWZNX5+fntyrxcrlcvPPOO2RlZXHkkUe2dXhKKaW6gKFDhxIdHc3HH3/MwIED/bZ98cUXZGVl+XU37ty502+fqKioRi1gRx99NHl5eYSFhdGvX79WxeVyuVi1ahXHH388ALt27WLv3r0cccQRB3xMIOcdOnQoK1as8FvX8H5nEbTEyxizHDhQc07TbaOdgNU8mpeXx+DBg1v8+DVr1rBv3z6uvvpqwsK0fq1SSqmWi4+P54YbbmD27NlER0dz0kknsX//ftasWcOgQYPIyclh0aJFjB07lvfff58XX3zR7/HZ2dns3LmTtWvX0rt3b+Lj4znttNM44YQTmDJlCvfffz9Dhgxh3759vPfee5x22mmMGzfuoHFFREQwa9YsHn74YWJjY/nDH/7AsGHDmp0OL5Dz/v73v+f444/nnnvu4YILLmDZsmW88cYbh/x7DAX95G+hpKQkIiMjWzXA3mrt6t69u9btUkopdUjuuecebrnlFubOncsRRxzB+eefz549ezj77LP505/+xKxZsxg5ciQffvghf/vb3/wee/7553PWWWcxYcIE0tPTefHFFxER3nnnHU499VRmzJjB4MGDmTp1Kps2baJHjx4BxRQdHc3tt9/OZZddxpgxY3C5XLz++uvNDqsJ5LzHHXccTz/9NI899hgjR47k9ddfZ86cOa3+3YWSdIZ+09GjR5tA64i0h7/97W+kpqbyu9/9rkWPW7t2LY8//ji/+c1v/AYfKqWUCp2NGzc22xWmArNgwQKuu+46KioqQh1Ku2ju70ZE1hhjRje1TVu8WiEzM7NVLV4ffvghmZmZjB7d5GuhlFJKqcOcJl6tkJGRQUFBwUEvzfXlcDjYvn07v/jFL3Rsl1JKqU7nl7/8JXa7vcnl7rvvDnV4nUa7VK4/3GRkZFBfX09RUVGjuiMHsmXLFowxDBo0KMjRKaWUUm3vqaeewuFwNLktJSWFlJQUrrjiivYNqhPSxKsVfK9sDDTx2rx5MxEREfTt2zeYoSmllFJBkZWVFeoQDgva59UKVuLVknFemzdvJjs7m6ioqGCFpZRSSqkOThOvVrDb7cTGxgY8M3p1dTW7du3SbkallFKqi9PEqxVEhMzMzIATry1btuByuTTxUkoppbo4TbxaKSMjI+Cuxs2bNxMeHk7//v2DHJVSSimlOjJNvFopMzOToqIinE7nQffV8V1KKaWUAk28Wi0jIwNjDAUFBc3uV11dzc6dO7WbUSmlVJf2448/MnbsWGJiYsjOzj7gusOdJl6t5FtSojnbtm3T8V1KKaWCZt26dYSHh3PCCSeELIbx48cjIo2Wiy66yLvPHXfcgc1m48cff2TVqlUHXHeosrOzmTdvXpscKxg08WqljIwM4OCJ16ZNmwgLC6Nfv37tEZZSSqku5sknn+S3v/0t33//PRs3bgxZHL/+9a/Jzc31Wx5//HHv9i1btnDiiSeSnZ3trYHZ1LrDnSZerRQbG0tCQsJBB9j/9NNP9OnTh5iYmHaKTCmlVFfhcDh44YUXmDFjBhdccAFPP/20d9vFF1/M+eef77e/y+WiV69ePPTQQwBUVlZy2WWXYbfbyczM5J577mHSpEmtqkBvs9no1q2b35KYmAi4qwF88803/O1vf0NEmDNnTpPrAHJycrjoootITk4mOTmZiRMn8tNPP/md6+2332bMmDHExsaSmprK2WefTXV1NePHj2fnzp386U9/8ra6dTRauf4QZGRkNNviVVNTw/bt2zn99NPbMSqllFJtYfz48Y3WTZ06ld/+9rdUVVVx1llnNdp+xRVXcMUVV1BYWMgFF1zQaPvMmTOZNm0au3fv5tJLL/XbtmzZshbHuHjxYvr06cPIkSO59NJLmTp1Kvfccw+RkZFccsklnH/++ZSUlJCUlATAp59+Sm5uLhdffDEAN954I59++ilvvPEGPXr0YO7cuXz++eece+65LY6lObm5uYwfP55JkyZx0003Ybfbufbaaxutq6qq4pRTTuH444/n008/JSoqinnz5nHaaaexceNGbDYb7733HlOmTOHWW2/l2Wefpa6ujg8++ACXy8Xrr7/OkUceyZVXXsnMmTPb9Dm0FW3xOgSZmZnNtnjp+C6llFLB9NRTT3kTuJNPPhmbzcabb74JwP/7f/+PhIQEXnvtNe/+ixYtYsKECXTr1o2KigqeeeYZ7rvvPk4//XSGDRvG008/TVhY61KDJ554otHk2Y8++igA3bp1IyIiArvdTrdu3bw/G6576aWXMMbw7LPPMnLkSIYMGcLjjz9ORUUFS5YsAWDu3LlccMEF3HXXXQwdOpSRI0dy0003YbPZSElJITw8nPj4eG+rW0ejLV6HIDMzky+++AKHw0FsbGyj7db4rgEDBoQgOqWUUoeiuRYom83W7Pa0tLRmt/fq1atVLVy+tmzZwhdffMGLL74IuLvzpk+fzlNPPcX5559PREQE06ZNY9GiRfzmN7+hpqaG1157jf/7v/8DYOvWrTidTo499ljvMePi4hg+fHir4pk2bRp//etf/da1dNzWmjVr2L59O/Hx8X7rq6qq2Lp1K+C+mKAzT8YdtMRLRJ4BJgH5xpjhnnVzgBmAVYPhNmPMO8GKIdisAfb5+fn06dOn0faffvqJ3r176/gupZRSbe6pp56ivr6e3r17e9cZYwDYvXs3vXr14pJLLuH4448nJyeHlStXUltb6+1GtPZtq3FQiYmJh9zQ4HK5OOqoo3jppZcabUtJSTmkY3cUwexqXACc2cT6h4wxR3mWTpt0QfMlJWpra9m+fbt2MyqllGpzdXV1LFy4kHvuuYf169d7l2+++YaRI0fy7LPPAjBmzBj69+/Piy++yKJFizjnnHOw2+0ADBgwgMjISL7++mvvcauqqvj+++9D8pwAjj76aLZs2UJaWhoDBgzwW6zEa9SoUXz88ccHPEZUVBT19fXtFXKLBS3xMsZ8BhQF6/gdQXp6OiLSZOK1bds26uvrNfFSSinV5t5++20KCwuZMWMGw4cP91suuuginnnmGVwuF4C3+/Htt9/mkksu8R7Dbrdz5ZVXcsstt/Dxxx+zYcMGrrrqKlwul18r2OzZs5kwYcJBY6qqqmLfvn1+S1FRy9KA6dOnk5mZyZQpU/j000/Zvn07n332GTfeeKP3ysbbb7+dV199lTvuuIMNGzbwww8/8NBDD1FVVQW463h9/vnn5OTkUFhYCLivlBwyZAhvvPFGi+IJhlAMrr9ORL4VkWdEJPlAO4nI1SKyWkRWH6w6fKhERkaSkpLS5AD7zZs3IyI6vksppVSbe/rppznllFNITU1ttO3CCy9k586dfPTRRwBccsklbNq0icTExEZX2c+bN49x48YxefJkTjnlFEaOHMno0aP9hsjk5uZ6x1c159lnn6V79+5+y+TJk1v0vGw2G5999hn9+vXjwgsvZMiQIVx++eUUFxeTnOxOGc466yzeeOMN3n33XUaNGsXJJ5/M0qVLvRcF/O1vf2P37t3079/fO8bM6XSyadMmSktLWxRPMIjVxxuUg4tkA0t8xnhlAoWAAeYC3Y0xVx7sOKNHjzarV68OWpyHYv78+TgcDmbPnu23/h//+Ae1tbXcfvvtIYpMKaVUIDZu3MgRRxwR6jA6hJqaGvr06cOf/vQnbrzxxlCH06E193cjImuMMaOb2tauLV7GmDxjTL0xxgU8CRx7sMd0dJmZmeTl5XkHKVZWVvLUU0+xZcsWRowYEeLolFJKqQNbt24dL7zwAlu2bGHdunVcfvnllJeXM23atFCHdthq13ISItLdGJPruXsuELoRfG0kMzMTh8NBeXk5OTk5LFiwgLKyMiZPnsyZZzZ1bYFSSinVcTz44INs2rSJiIgIjjrqKD777DN69uwZ6rAOW8EsJ/EiMB5IE5E9wF+B8SJyFO6uxh3ANcE6f3uxSkosWLCAH374gW7dujFz5swuM8u6UkqpzmvUqFF01KE8h6ugJV7GmIubWP10E+s6NaukxA8//MCpp57KueeeS1RUVIijUkoppVRHpJXrD1FaWhqTJ0+mX79+OjhTKaU6KWNMh5xQWXVMh3JhoiZeh0hEmDhxYqjDUEop1UqRkZE4HA5sNluoQ1GdhMPhIDIyslWP1UmylVJKdWkZGRnk5ORQVVV1SC0Z6vBnjKGqqoqcnBzvGO+W0hYvpZRSXVpCQgIAe/fuxel0hjga1dFFRkaSmZnp/btpKU28lFJKdXkJCQmt/iBVqiW0q1EppZRSqp1o4qWUUkop1U408VJKKaWUaieaeCmllFJKtRNNvJRSSiml2ol0hpolIlIA7AzyadKAwiCfQ7Wcvi4dj74mHZO+Lh2PviYdU3u8Ln2MMelNbegUiVd7EJHVxpjRoY5D+dPXpePR16Rj0tel49HXpGMK9euiXY1KKaWUUu1EEy+llFJKqXaiidfPngh1AKpJ+rp0PPqadEz6unQ8+pp0TCF9XXSMl1JKKaVUO9EWL6WUUkqpdqKJl1JKKaVUO9HECxCRM0Vkk4hsEZFbQx1PVyQivURkqYhsFJEfROQGz/oUEflQRH7y/EwOdaxdjYiEi8g6EVniua+vSYiJSJKILBaRHz3/M2P1dQktEfmD573rexF5UURi9DVpfyLyjIjki8j3PusO+DqIyGzPZ/8mEfl/7RFjl0+8RCQceAT4JTAUuFhEhoY2qi6pDrjRGHMEcBzwO8/rcCvwsTFmIPCx575qXzcAG33u62sSeg8D7xljhgBH4n599HUJERHJAn4PjDbGDAfCgYvQ1yQUFgBnNljX5Ovg+Yy5CBjmecyjnpwgqLp84gUcC2wxxmwzxtQCLwFTQhxTl2OMyTXGrPXcLsf9QZKF+7VY6NltIXBOSALsokSkJzAReMpntb4mISQiCcBJwNMAxphaY0wJ+rqEWgQQKyIRgA3Yi74m7c4Y8xlQ1GD1gV6HKcBLxpgaY8x2YAvunCCoNPFyf7jv9rm/x7NOhYiIZAOjgJVApjEmF9zJGZARwtC6ovnAzYDLZ52+JqHVDygAnvV0AT8lInHo6xIyxpgcYB6wC8gFSo0xH6CvSUdxoNchJJ//mniBNLFOa2yEiIjYgdeAWcaYslDH05WJyCQg3xizJtSxKD8RwNHAY8aYUUAl2oUVUp4xQ1OAvkAPIE5ELgltVCoAIfn818TLneH28rnfE3cTsWpnIhKJO+laZIx53bM6T0S6e7Z3B/JDFV8XdAIwWUR24O6CP1VEnkdfk1DbA+wxxqz03F+MOxHT1yV0TgO2G2MKjDFO4HXgePQ16SgO9DqE5PNfEy9YBQwUkb4iEoV7oN2bIY6pyxERwT1mZaMx5kGfTW8Cl3tuXw78r71j66qMMbONMT2NMdm4/y8+McZcgr4mIWWM2QfsFpHBnlUTgA3o6xJKu4DjRMTmeS+bgHucqr4mHcOBXoc3gYtEJFpE+gIDga+DHYxWrgdE5CzcY1nCgWeMMX8PbURdj4icCHwOfMfP44luwz3O6xWgN+43twuNMQ0HTqogE5HxwE3GmEkikoq+JiElIkfhvuAhCtgG/Br3F2l9XUJERO4EpuG+QnsdcBVgR1+TdiUiLwLjgTQgD/gr8F8O8DqIyO3Albhft1nGmHeDHqMmXkoppZRS7UO7GpVSSiml2okmXkoppZRS7UQTL6WUUkqpdqKJl1JKKaVUO9HESymllFKqnWjipZTq1EQkVUTWe5Z9IpLjcz+qFcc7X0R+EJHPPaUzEJH+IvJS20evlOpqtJyEUuqwISJzgApjzLxDOMaXwP/DXTQ2xhjzT09toL8YY35qm0iVUl2VtngppQ47IjLBM4H0dyLyjIhEe9bvEJH7RORrzzKgiYe7gGjABjhFZByQq0mXUqotaOKllDrcxAALgGnGmBG4J5We6bO9zBhzLPAv3DNWNHQn8D7u+fdeBO4A5gYxXqVUF6KJl1LqcBOOe8LizZ77C4GTfLa/6PNzbMMHG2M+NMYcY4w5GzgHeAcYLCKLReRJEbEFL3Sl1OFOEy+l1OGm8iDbzQFu+/EkWJcDjwL34J7PbQ0w/VADVEp1XZp4KaUONzFAts/4rUuBT322T/P5+VUzx7kZeNgY4wRicSdpLtxjv5RSqlUiQh2AUkq1sWrg18CrIhIBrAL+7bM9WkRW4v7ieXFTBxCRHsBoY8wcz6oHgBVACe7uR6WUahUtJ6GU6jJEZAfuhKow1LEopbom7WpUSimllGon2uKllFJKKdVOtMVLKaWUUqqdaOKllFJKKdVONPFSSimllGonmngppZRSSrUTTbyUUkoppdrJ/wfkW/gsEfPG9gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "for m in [\"rand_m_pred\", \"ml_pred\", \"cate_pred\"]:\n",
    "    cumu_effect = cumulative_effect_curve(test_pred, m, \"sales\", \"discounts\", steps=100)\n",
    "    x = np.array(range(len(cumu_effect)))\n",
    "    plt.plot(100*(x/x.max()), cumu_effect, label=m)\n",
    "\n",
    "plt.hlines(effect(test_pred, \"sales\", \"discounts\"), 0, 100, linestyles=\"--\", color=\"black\", label=\"Avg. Effect.\")\n",
    "plt.xlabel(\"Top %\")\n",
    "plt.ylabel(\"Cumulative Effect\")\n",
    "plt.title(\"Cumulative Effect Curve\")\n",
    "plt.legend(fontsize=14)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6d7fc9f",
   "metadata": {},
   "source": [
    "## Cumulative Gain\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7f6c0cf1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:43.090974Z",
     "start_time": "2023-06-26T13:25:42.941598Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.50387597,  0.982917  , ..., 31.82346463, 32.00615008,\n",
       "       32.16196368])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cumulative_gain_curve(df, prediction, y, t,\n",
    "                          ascending=False, normalize=False, steps=100):\n",
    "    \n",
    "    effect_fn = effect(t=t, y=y)\n",
    "    normalizer = effect_fn(df) if normalize else 0\n",
    "    \n",
    "    size = len(df)\n",
    "    ordered_df = (df\n",
    "                  .sort_values(prediction, ascending=ascending)\n",
    "                  .reset_index(drop=True))\n",
    "    \n",
    "    steps = np.linspace(size/steps, size, steps).round(0)\n",
    "    effects = [(effect_fn(ordered_df.query(f\"index<={row}\"))\n",
    "                -normalizer)*(row/size) \n",
    "               for row in steps]\n",
    "\n",
    "    return np.array([0] + effects)\n",
    "\n",
    "\n",
    "cumulative_gain_curve(test_pred, \"cate_pred\", \"sales\", \"discounts\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "80e10e23",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:43.882070Z",
     "start_time": "2023-06-26T13:25:43.092375Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Cumulative Gain Curve (Normalized)')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15,5))\n",
    "\n",
    "for m in [\"rand_m_pred\", \"ml_pred\", \"cate_pred\"]:\n",
    "    cumu_gain = cumulative_gain_curve(test_pred, m, \"sales\", \"discounts\")\n",
    "    x = np.array(range(len(cumu_gain)))\n",
    "    ax1.plot(100*(x/x.max()), cumu_gain, label=m)\n",
    "    \n",
    "ax1.plot([0, 100], [0, effect(test_pred, \"sales\", \"discounts\")], linestyle=\"--\", label=\"Random Model\", color=\"black\")\n",
    "\n",
    "ax1.set_xlabel(\"Top %\")\n",
    "ax1.set_ylabel(\"Cumulative Gain\")\n",
    "ax1.set_title(\"Cumulative Gain Curve\")\n",
    "ax1.legend()\n",
    "\n",
    "\n",
    "for m in [\"rand_m_pred\", \"ml_pred\", \"cate_pred\"]:\n",
    "    cumu_gain = cumulative_gain_curve(test_pred, m, \"sales\", \"discounts\", normalize=True)\n",
    "    x = np.array(range(len(cumu_gain)))\n",
    "    ax2.plot(100*(x/x.max()), cumu_gain, label=m)\n",
    "    \n",
    "ax2.hlines(0, 0, 100, linestyle=\"--\", label=\"Random Model\", color=\"black\")\n",
    "\n",
    "ax2.set_xlabel(\"Top %\")\n",
    "ax2.set_ylabel(\"Cumulative Gain\")\n",
    "ax2.set_title(\"Cumulative Gain Curve (Normalized)\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "630d464c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.206516Z",
     "start_time": "2023-06-26T13:25:43.883418Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AUC for rand_m_pred: 6.0745233598544495\n",
      "AUC for ml_pred: -45.44063124684\n",
      "AUC for cate_pred: 181.74573239200615\n"
     ]
    }
   ],
   "source": [
    "for m in [\"rand_m_pred\", \"ml_pred\", \"cate_pred\"]:\n",
    "    gain = cumulative_gain_curve(test_pred, m,\n",
    "                                 \"sales\", \"discounts\", normalize=True)\n",
    "    print(f\"AUC for {m}:\", sum(gain))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5134634b",
   "metadata": {},
   "source": [
    "## Target Transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cbf3bc4d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.262424Z",
     "start_time": "2023-06-26T13:25:44.207570Z"
    }
   },
   "outputs": [],
   "source": [
    "X = [\"C(month)\", \"C(weekday)\", \"is_holiday\", \"competitors_price\"]\n",
    "\n",
    "y_res = smf.ols(f\"sales ~ {'+'.join(X)}\", data=test).fit().resid\n",
    "t_res = smf.ols(f\"discounts ~ {'+'.join(X)}\", data=test).fit().resid\n",
    "\n",
    "tau_hat = y_res/t_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ef036f7e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.267671Z",
     "start_time": "2023-06-26T13:25:44.263550Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for rand_m_pred: 1115.803515760459\n",
      "MSE for ml_pred: 576256.7425385397\n",
      "MSE for cate_pred: 42.90447405550281\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "for m in [\"rand_m_pred\", \"ml_pred\", \"cate_pred\"]:\n",
    "    wmse = mean_squared_error(tau_hat, test_pred[m],\n",
    "                              sample_weight=t_res**2)\n",
    "    print(f\"MSE for {m}:\", wmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e92b278a",
   "metadata": {},
   "source": [
    "## When Prediction Models are Good for Effect Ordering\n",
    " \n",
    "### Marginal Decreasing Returns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dd9dcc16",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.342118Z",
     "start_time": "2023-06-26T13:25:44.269282Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'T')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "n = 1000\n",
    "t = np.random.uniform(1, 30, size=n)\n",
    "y = np.random.normal(10+3*np.log(t), size=n)\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.scatter(t, y)\n",
    "plt.ylabel(\"Y\")\n",
    "plt.xlabel(\"T\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a2bc99",
   "metadata": {},
   "source": [
    "### Binary Outcomes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84934f6d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.663150Z",
     "start_time": "2023-06-26T13:25:44.343590Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "n = 10000\n",
    "t = np.random.uniform(1, 30, size=n).round(1)\n",
    "y = (np.random.normal(t, 5, size=n) > 15).astype(int)\n",
    "\n",
    "df_sim = pd.DataFrame(dict(t=t, y=y)).groupby(\"t\")[\"y\"].mean().reset_index()\n",
    "df_sim\n",
    "\n",
    "ax1.scatter(df_sim[\"t\"], df_sim[\"y\"])\n",
    "ax1.set_ylabel(\"Y\")\n",
    "ax1.set_xlabel(\"T\")\n",
    "\n",
    "\n",
    "n = 10000\n",
    "t = np.random.exponential(1, n).round(1).clip(0, 8)\n",
    "y = (np.random.normal(t, 2, size=n) > 6).astype(int)\n",
    "\n",
    "df_sim = (pd.DataFrame(dict(t=t, y=y, size=1))\n",
    "          .query(\"t<6\")\n",
    "          .groupby(\"t\")\n",
    "          .agg({\"y\":\"mean\", \"size\":\"sum\"})\n",
    "          .reset_index())\n",
    "\n",
    "sns.scatterplot(data=df_sim, y=\"y\", x=\"t\", size=\"size\", ax=ax2, sizes=(5,100))\n",
    "ax2.set_ylabel(\"Default Prob.\")\n",
    "ax2.set_xlabel(\"Loan (in 100k)\")\n",
    "\n",
    "\n",
    "n = 10000\n",
    "t = np.random.beta(2, 2, n).round(2)*10\n",
    "y = (np.random.normal(5+t, 4, size=n) > 0).astype(int)\n",
    "\n",
    "df_sim = (pd.DataFrame(dict(t=t, y=y, size=1))\n",
    "          .groupby(\"t\")\n",
    "          .agg({\"y\":\"mean\", \"size\":\"sum\"})\n",
    "          .reset_index())\n",
    "\n",
    "sns.scatterplot(data=df_sim, y=\"y\", x=\"t\", size=\"size\", ax=ax3, sizes=(5,100))\n",
    "ax3.set_ylabel(\"Conversion\")\n",
    "ax3.set_xlabel(\"Discount (%)\")\n",
    "plt.tight_layout()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec8a9961",
   "metadata": {},
   "source": [
    "## CATE for Decision Making\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1c8e2014",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.782782Z",
     "start_time": "2023-06-26T13:25:44.664436Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fcb8a3fe490>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def demand(price, tau):\n",
    "    return 50-tau*price\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))\n",
    "\n",
    "prices = np.linspace(1, 15)\n",
    "\n",
    "for i, tau in enumerate([1, 2, 3]):\n",
    "    q = demand(prices, tau)\n",
    "    ax1.plot(prices, q, color=f\"C{i}\", label=f\"te={tau}\")\n",
    "    ax2.plot(prices, q*prices, color=f\"C{i}\", label=f\"te={tau}\")\n",
    "\n",
    "ax1.set_ylabel(\"Demand\")\n",
    "ax1.set_xlabel(\"Price\")\n",
    "\n",
    "ax2.set_ylabel(\"Revenues\")\n",
    "ax2.set_xlabel(\"Price\")\n",
    "\n",
    "ax1.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ff1da5f8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-06-26T13:25:44.923626Z",
     "start_time": "2023-06-26T13:25:44.784148Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cost(q):\n",
    "    return q*3\n",
    "\n",
    "def profit(price, tau):\n",
    "    q = demand(price, tau)\n",
    "    return q*price - cost(q)\n",
    "\n",
    "prices = np.linspace(1, 30)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))\n",
    "\n",
    "for i, tau in enumerate([1, 2, 3]):\n",
    "    profits = profit(prices, tau)\n",
    "    \n",
    "    max_price = prices[np.argmax(profits)]\n",
    "    \n",
    "    ax1.plot(prices, cost(demand(prices, tau)), label=f\"te={tau}\")\n",
    "    \n",
    "    ax2.plot(prices, profits, color=f\"C{i}\", label=f\"te={tau}\")\n",
    "    ax2.vlines(max_price, 0, max(profits), color=f\"C{i}\", linestyle=\"--\")\n",
    "    ax2.set_ylim(-400, 600)\n",
    "    \n",
    "\n",
    "ax2.hlines(0, 0, max(prices), color=\"black\")\n",
    "# ax2.legend()\n",
    "ax2.set_ylabel(\"Profits\")\n",
    "ax2.set_xlabel(\"Price\");\n",
    "\n",
    "ax1.legend()\n",
    "ax1.set_ylabel(\"Cost\")\n",
    "ax1.set_xlabel(\"Price\")\n",
    "\n",
    "plt.tight_layout()\n"
   ]
  },
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    "## Key Ideas\n"
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